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- La ecuación:
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Ecuación x^3-x^2-x-1=0
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Ecuación 3x-2(3x+4)=10
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Ecuación 12-4(x-3)=39-9x
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Ecuación 0,2x+2,7=1,4-1,1x
- Expresar {x} en función de y en la ecuación:
- -11*x-3*y=14
- 2*x-15*y=-1
- -18*x-6*y=-1
- 6*x+9*y=-9
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Expresiones idénticas
- dos *x- uno /x- cinco - tres *x+ dos /x+ cuatro = catorce *x+ once /x^ dos -x- veinte
- 2 multiplicar por x menos 1 dividir por x menos 5 menos 3 multiplicar por x más 2 dividir por x más 4 es igual a 14 multiplicar por x más 11 dividir por x al cuadrado menos x menos 20
- dos multiplicar por x menos uno dividir por x menos cinco menos tres multiplicar por x más dos dividir por x más cuatro es igual a cotangente de angente de orce multiplicar por x más once dividir por x en el grado dos menos x menos veinte
- 2*x-1/x-5-3*x+2/x+4=14*x+11/x2-x-20
- 2*x-1/x-5-3*x+2/x+4=14*x+11/x²-x-20
- 2*x-1/x-5-3*x+2/x+4=14*x+11/x en el grado 2-x-20
- 2x-1/x-5-3x+2/x+4=14x+11/x^2-x-20
- 2x-1/x-5-3x+2/x+4=14x+11/x2-x-20
- 2*x-1 dividir por x-5-3*x+2 dividir por x+4=14*x+11 dividir por x^2-x-20
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Expresiones semejantes
- 2*x-1/x-5-3*x+2/x+4=14*x+11/x^2-x+20
- 2*x-1/x-5-3*x+2/x+4=14*x-11/x^2-x-20
- 2*x-1/x-5-3*x+2/x-4=14*x+11/x^2-x-20
- 2*x+1/x-5-3*x+2/x+4=14*x+11/x^2-x-20
- 2x-1/(x-5)-(3x+2)/x+4=(14x+11)/(x^2-x-20)
- 2*x-1/x-5-3*x+2/x+4=14*x+11/x^2+x-20
- 2*x-1/x+5-3*x+2/x+4=14*x+11/x^2-x-20
- 2*x-1/x-5+3*x+2/x+4=14*x+11/x^2-x-20
- 2*x-1/x-5-3*x-2/x+4=14*x+11/x^2-x-20
2*x-1/x-5-3*x+2/x+4=14*x+11/x^2-x-20 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
1 2 11
2*x - - - 5 - 3*x + - + 4 = 14*x + -- - x - 20
x x 2
x
$$\left(\left(- 3 x + \left(\left(2 x - \frac{1}{x}\right) - 5\right)\right) + \frac{2}{x}\right) + 4 = \left(- x + \left(14 x + \frac{11}{x^{2}}\right)\right) - 20$$
Respuesta rápida
[src]
______________________ / ______________________\
/ ________ | / ________ |
/ 10525 3*\/ 856353 | ___ / 10525 3*\/ 856353 |
3 / ----- + ------------ | ___ \/ 3 *3 / ----- + ------------ |
19 \/ 1372 392 403 | 403*\/ 3 \/ 1372 392 |
x1 = -- + --------------------------- + -------------------------------- + I*|- -------------------------------- + ---------------------------------|
42 6 ______________________ | ______________________ 6 |
/ ________ | / ________ |
/ 10525 3*\/ 856353 | / 10525 3*\/ 856353 |
1176*3 / ----- + ------------ | 1176*3 / ----- + ------------ |
\/ 1372 392 \ \/ 1372 392 /
$$x_{1} = \frac{403}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{19}{42} + i \left(- \frac{403 \sqrt{3}}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6}\right)$$
______________________ / ______________________ \
/ ________ | / ________ |
/ 10525 3*\/ 856353 | ___ / 10525 3*\/ 856353 |
3 / ----- + ------------ | \/ 3 *3 / ----- + ------------ ___ |
19 \/ 1372 392 403 | \/ 1372 392 403*\/ 3 |
x2 = -- + --------------------------- + -------------------------------- + I*|- --------------------------------- + --------------------------------|
42 6 ______________________ | 6 ______________________|
/ ________ | / ________ |
/ 10525 3*\/ 856353 | / 10525 3*\/ 856353 |
1176*3 / ----- + ------------ | 1176*3 / ----- + ------------ |
\/ 1372 392 \ \/ 1372 392 /
$$x_{2} = \frac{403}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{19}{42} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{403 \sqrt{3}}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}\right)$$
______________________
/ ________
/ 10525 3*\/ 856353
3 / ----- + ------------
19 403 \/ 1372 392
x3 = -- - ------------------------------- - ---------------------------
42 ______________________ 3
/ ________
/ 10525 3*\/ 856353
588*3 / ----- + ------------
\/ 1372 392
$$x_{3} = - \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{3} - \frac{403}{588 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{19}{42}$$
x3 = -(3*sqrt(856353)/392 + 10525/1372)^(1/3)/3 - 403/(588*(3*sqrt(856353)/392 + 10525/1372)^(1/3)) + 19/42
Suma y producto de raíces
[src]
suma
______________________ / ______________________\ ______________________ / ______________________ \ ______________________
/ ________ | / ________ | / ________ | / ________ | / ________
/ 10525 3*\/ 856353 | ___ / 10525 3*\/ 856353 | / 10525 3*\/ 856353 | ___ / 10525 3*\/ 856353 | / 10525 3*\/ 856353
3 / ----- + ------------ | ___ \/ 3 *3 / ----- + ------------ | 3 / ----- + ------------ | \/ 3 *3 / ----- + ------------ ___ | 3 / ----- + ------------
19 \/ 1372 392 403 | 403*\/ 3 \/ 1372 392 | 19 \/ 1372 392 403 | \/ 1372 392 403*\/ 3 | 19 403 \/ 1372 392
-- + --------------------------- + -------------------------------- + I*|- -------------------------------- + ---------------------------------| + -- + --------------------------- + -------------------------------- + I*|- --------------------------------- + --------------------------------| + -- - ------------------------------- - ---------------------------
42 6 ______________________ | ______________________ 6 | 42 6 ______________________ | 6 ______________________| 42 ______________________ 3
/ ________ | / ________ | / ________ | / ________ | / ________
/ 10525 3*\/ 856353 | / 10525 3*\/ 856353 | / 10525 3*\/ 856353 | / 10525 3*\/ 856353 | / 10525 3*\/ 856353
1176*3 / ----- + ------------ | 1176*3 / ----- + ------------ | 1176*3 / ----- + ------------ | 1176*3 / ----- + ------------ | 588*3 / ----- + ------------
\/ 1372 392 \ \/ 1372 392 / \/ 1372 392 \ \/ 1372 392 / \/ 1372 392
$$\left(- \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{3} - \frac{403}{588 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{19}{42}\right) + \left(\left(\frac{403}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{19}{42} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{403 \sqrt{3}}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}\right)\right) + \left(\frac{403}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{19}{42} + i \left(- \frac{403 \sqrt{3}}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6}\right)\right)\right)$$
=
/ ______________________\ / ______________________ \
| / ________ | | / ________ |
| ___ / 10525 3*\/ 856353 | | ___ / 10525 3*\/ 856353 |
| ___ \/ 3 *3 / ----- + ------------ | | \/ 3 *3 / ----- + ------------ ___ |
19 | 403*\/ 3 \/ 1372 392 | | \/ 1372 392 403*\/ 3 |
-- + I*|- -------------------------------- + ---------------------------------| + I*|- --------------------------------- + --------------------------------|
14 | ______________________ 6 | | 6 ______________________|
| / ________ | | / ________ |
| / 10525 3*\/ 856353 | | / 10525 3*\/ 856353 |
| 1176*3 / ----- + ------------ | | 1176*3 / ----- + ------------ |
\ \/ 1372 392 / \ \/ 1372 392 /
$$\frac{19}{14} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{403 \sqrt{3}}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}\right) + i \left(- \frac{403 \sqrt{3}}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6}\right)$$
producto
/ ______________________ / ______________________\\ / ______________________ / ______________________ \\ / ______________________\ | / ________ | / ________ || | / ________ | / ________ || | / ________ | | / 10525 3*\/ 856353 | ___ / 10525 3*\/ 856353 || | / 10525 3*\/ 856353 | ___ / 10525 3*\/ 856353 || | / 10525 3*\/ 856353 | | 3 / ----- + ------------ | ___ \/ 3 *3 / ----- + ------------ || | 3 / ----- + ------------ | \/ 3 *3 / ----- + ------------ ___ || | 3 / ----- + ------------ | |19 \/ 1372 392 403 | 403*\/ 3 \/ 1372 392 || |19 \/ 1372 392 403 | \/ 1372 392 403*\/ 3 || |19 403 \/ 1372 392 | |-- + --------------------------- + -------------------------------- + I*|- -------------------------------- + ---------------------------------||*|-- + --------------------------- + -------------------------------- + I*|- --------------------------------- + --------------------------------||*|-- - ------------------------------- - ---------------------------| |42 6 ______________________ | ______________________ 6 || |42 6 ______________________ | 6 ______________________|| |42 ______________________ 3 | | / ________ | / ________ || | / ________ | / ________ || | / ________ | | / 10525 3*\/ 856353 | / 10525 3*\/ 856353 || | / 10525 3*\/ 856353 | / 10525 3*\/ 856353 || | / 10525 3*\/ 856353 | | 1176*3 / ----- + ------------ | 1176*3 / ----- + ------------ || | 1176*3 / ----- + ------------ | 1176*3 / ----- + ------------ || | 588*3 / ----- + ------------ | \ \/ 1372 392 \ \/ 1372 392 // \ \/ 1372 392 \ \/ 1372 392 // \ \/ 1372 392 /
$$\left(\frac{403}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{19}{42} + i \left(- \frac{403 \sqrt{3}}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6}\right)\right) \left(\frac{403}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{19}{42} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{403 \sqrt{3}}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{3} - \frac{403}{588 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{19}{42}\right)$$
=
-11 ---- 14
$$- \frac{11}{14}$$
-11/14
Respuesta numérica
[src]
x1 = 1.00087393302137 + 0.466003755108876*i
x2 = 1.00087393302137 - 0.466003755108876*i
x3 = -0.644605008899888
x3 = -0.644605008899888